Order of a Matrix

Let’s consider the matrix

It has 2 rows & 2 columns

So, we write the order as

And,

  3, 2, 1, 4 are elements of matrix A

We write the matrix A as

Where

a ₁₁ → element in 1st row, 1st column

a ₁₂ → element in 1st row, 2nd column

a ₂₁ → element in 2nd row, 1st column

a ₂₂ → element in 2nd row, 2nd column

So,

    a ₁₁ = 3

    a ₁₂ = 2

    a ₂₁ = 1

    a ₂₂ = 4

For matrix

It has 3 rows & 2 columns

So, the order is 3 × 2.

We write matrix B as

Similarly,

Create a 4 × 3 matrix where elements are given by

a _ij = i + j

A 4 × 3 matrix looks like

Now,

a ₁₁ = 1 + 1 = 2

a ₁₂ = 1 + 2 = 3

a ₁₃ = 1 + 3 = 4

a ₂₁ = 2 + 1 = 3

a ₂₂ = 2 + 2 = 4

a ₂₃ = 2 + 3 = 5

a ₃₂ = 3 + 2 = 5

a ₃₃ = 3 + 3 = 6

a ₄₁ = 4 + 1 = 5

a ₄₂ = 4 + 2 = 5

a ₄₃ = 4 + 3 = 7

So, our matrix is